function q46()
{
$number = 1;
while (true) {
$number += 2;
if (IntegerFactorization::isPrime($number)) {
continue;
}
// Try squares in ascending order and test whether the difference between the current number
// and this double square is a prime
// If we find a working combination (prime + double square), then this number is not the one we're looking for
// If we find no combination of a square + prime up to the number, then it is the number we are looking for
$found = false;
$square = 1;
$doubleSquare = 2 * $square * $square;
while ($doubleSquare <= $number) {
$complement = $number - $doubleSquare;
if (IntegerFactorization::isPrime($complement)) {
$found = true;
break;
}
++$square;
$doubleSquare = 2 * $square * $square;
}
if (!$found) {
break;
}
}
return $number;
}
function q21($from, $to)
{
$integerToSum = [];
for ($i = $from; $i < $to; ++$i) {
$primeDecomposition = IntegerFactorization::solve($i);
$sumOfDivisors = Math::divisorsSum($primeDecomposition);
$sumOfProperDivisors = $sumOfDivisors - $i;
$integerToSum[$i] = $sumOfProperDivisors;
}
$sumOfAmicableNumbers = 0;
foreach ($integerToSum as $integer => $sum) {
if ($integer !== $sum && isset($integerToSum[$sum]) && $integerToSum[$sum] === $integer) {
$sumOfAmicableNumbers += $integerToSum[$integer] + $integerToSum[$sum];
unset($integerToSum[$integer]);
unset($integerToSum[$sum]);
}
}
return $sumOfAmicableNumbers;
}
public static function greatestCommonDivisor(array $numbers)
{
if (empty($numbers)) {
throw new LogicException('Cannot obtain greatest common divisor on an empty array.');
}
$factors = [];
foreach ($numbers as $number) {
$decomposition = IntegerFactorization::solve($number);
foreach ($decomposition as $prime => $count) {
$factors[$prime][] = $count;
}
}
$total = 1;
foreach ($factors as $prime => $counts) {
if (count($counts) === 1) {
continue;
}
sort($counts);
$total *= $prime ** $counts[0];
}
return $total;
}
/**
* @param int $n
* @return bool
*/
public static function isTruncatablePrime($n)
{
if (!IntegerFactorization::isPrime($n)) {
return false;
}
$stringRepresentation = (string) $n;
$stringRepresentationLength = strlen($stringRepresentation);
// Left to right
for ($i = 1; $i < $stringRepresentationLength; ++$i) {
$number = substr($stringRepresentation, $i);
if (!IntegerFactorization::isPrime($number)) {
return false;
}
}
// Right to left
for ($i = 1; $i < $stringRepresentationLength; ++$i) {
$number = substr($stringRepresentation, 0, $i);
if (!IntegerFactorization::isPrime($number)) {
return false;
}
}
return true;
}
